56 200microwave Trainer

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(1)e-learning. Electricity & Electronics. Control & Instrumentation. Process Control. Mechatronics. Telecommunications. Microwave Trainer 56-200. Electrical Power & Machines. Test & Measurement. Technology Training for tomorrows world.

(2) Microwave Trainer 56-200. Feedback Instruments Ltd, Park Road, Crowborough, E. Sussex, TN6 2QR, UK. Telephone: +44 (0) 1892 653322, Fax: +44 (0) 1892 663719. email: [email protected] website: http://www.fbk.com Manual: 56-200 Ed05 042005. Printed in England by Fl Ltd, Crowborough. Feedback Part No. 1160–56200.

(3) Notes.

(4) MICROWAVE TRAINER. Preface. THE HEALTH AND SAFETY AT WORK ACT 1974 We are required under the Health and Safety at Work Act 1974, to make available to users of this equipment certain information regarding its safe use.+ The equipment, when used in normal or prescribed applications within the parameters set for its mechanical and electrical performance, should not cause any danger or hazard to health or safety if normal engineering practices are observed and they are used in accordance with the instructions supplied. If, in specific cases, circumstances exist in which a potential hazard may be brought about by careless or improper use, these will be pointed out and the necessary precautions emphasised. While we provide the fullest possible user information relating to the proper use of this equipment, if there is any doubt whatsoever about any aspect, the user should contact the Product Safety Officer at Feedback Instruments Limited, Crowborough. This equipment should not be used by inexperienced users unless they are under supervision. We are required by European Directives to indicate on our equipment panels certain areas and warnings that require attention by the user. These have been indicated in the specified way by yellow labels with black printing, the meaning of any labels that may be fixed to the instrument are shown below:. CAUTION RISK OF DANGER. CAUTION ELECTROSTATIC SENSITIVE DEVICE. CAUTION RISK OF ELECTRIC SHOCK. Refer to accompanying documents. PRODUCT IMPROVEMENTS We maintain a policy of continuous product improvement by incorporating the latest developments and components into our equipment, even up to the time of dispatch. All major changes are incorporated into up-dated editions of our manuals and this manual was believed to be correct at the time of printing. However, some product changes which do not affect the instructional capability of the equipment, may not be included until it is necessary to incorporate other significant changes.. COMPONENT REPLACEMENT Where components are of a ‘Safety Critical’ nature, i.e. all components involved with the supply or carrying of voltages at supply potential or higher, these must be replaced with components of equal international safety approval in order to maintain full equipment safety. In order to maintain compliance with international directives, all replacement components should be identical to those originally supplied. Any component may be ordered direct from Feedback or its agents by quoting the following information:. 1.. Equipment type. 2.. Component value. 3. Component reference 4. Equipment serial number Components can often be replaced by alternatives available locally, however we cannot therefore guarantee continued performance either to published specification or compliance with international standards.. 56-200. i.

(5) MICROWAVE TRAINER. Preface. OPERATING CONDITIONS WARNING: This equipment must not be used in conditions of condensing humidity.. This equipment is designed to operate under the following conditions: Operating Temperature. 10°C to 40°C (50°F to 104°F). Humidity. 10% to 90% (non-condensing). DECLARATION CONCERNING ELECTROMAGNETIC COMPATIBILITY Should this equipment be used outside the classroom, laboratory study area or similar such place for which it is designed and sold then Feedback Instruments Ltd hereby states that conformity with the protection requirements of the European Community Electromagnetic Compatibility Directive (89/336/EEC) may be invalidated and could lead to prosecution. This equipment, when operated in accordance with the supplied documentation, does not cause electromagnetic disturbance outside its immediate electromagnetic environment.. COPYRIGHT NOTICE. © Feedback Instruments Limited All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Feedback Instruments Limited.. ACKNOWLEDGEMENTS Feedback Instruments Ltd acknowledge all trademarks. IBM, IBM - PC are registered trademarks of International Business Machines. MICROSOFT, WINDOWS XP, WINDOWS 2000, WINDOWS ME, WINDOWS NT, WINDOWS 98, WINDOWS 95 and Internet Explorer are registered trademarks of Microsoft Corporation.. ii. 56-200.

(6) MICROWAVE TRAINER. Contents. TABLE OF CONTENTS. 1. Introduction and Description. 1-1. 2. Assignments. 2-1. 3. 1. Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. 2-1-1. 2. Measurement of Voltage and Standing Wave Ratio (VSWR). 2-2-1. 3. Measurement of Diode Detector Law. 2-3-1. 4. Measurement of Impedance and Impedance Matching. 2-4-1. 5. Horn Antenna Investigations. 2-5-1. 6. Use of a Directional Coupler in Power Transmission and Reflected Measurements. 2-6-1. 7. Series, Shunt and Hybrid T Junctions. 2-7-1. 8. Waveguide to Coaxial Transformers. 2-8-1. 9. Microwave Radio Link Investigations. 2-9-1. Introduction to Microwaves and their Applications. 3-1. Appendices A. General, RF and Microwave – Data and Tables. A-1. B. Review of Transmission Line Theory. B-1. C. The Smith Impedance Chart and Applications. C-1. 56-200. TOC1.

(7) MICROWAVE TRAINER. Contents Notes. TOC 2. 56-200.

(8) Chapter 1 MICROWAVE TRAINER. Introduction and Description. 1 The microwave trainer, system and components. 1.1. Introduction. The Feedback 56-200 is a microwave trainer which enables students to familiarise themselves with the basics waveguide components making up microwave systems. It is an easy-to-use bench-top system, which is completely self-contained. It allows students to undertake microwave measurements and investigate the working of components making up the radio frequency transmission sections of microwave radio transmitters and receivers and radar systems. The trainer and manual provide the means for students to gain a working knowledge of microwaves and their applications and carry out basic microwave systems practical studies. The manual is written in a straightforward, clear style, and the trainer is suitable for technician and degree-level training and study. 1.2 Equipment The trainer comprises a set of waveguide components and a console that contains the microwave source power supply and circuits associated with measuring microwave power and signal strength. The components and source are designed in standard waveguide size WG16 that operates in the X-band range 8.2 to 12.4 GHz, a very important band for microwave radio, satellite communications and radar applications. The source itself operates at a fixed frequency of 10.425 GHz. The components shown in their packing-case positions are illustrated in Figure 1.1 and the complete list is given in paragraph 1.3.. 56-200. 1-1.

(9) Chapter 1 MICROWAVE TRAINER. Introduction and Description. 1.3 System Components Quantity. Identity No.. Description System waveguide: WG16 (WR90) which has the following specification: Internal dimensions: 0.9" x 0.4" or 22.86 x 10.16 mm H10 cut-off frequency and wavelength: 6.56 GHz, 45.7 mm Normal operating range: 8.2 to 12.4 GHz. 1. P. X-band CW FET Dielectric Resonant Oscillator (DRO) Source Frequency: fixed 10.425 GHz Output power: 10 mW minimum. 1-2. 2. A. Variable attenuators, resistive vane-central slot type; used to set attenuation level and control power transmission in waveguides. Maximum attenuation at vane setting 0° approx. 36 dB; minimum at 90° less than 1 dB. 1. B. Waveguide slotted line, for sampling electric field pattern in waveguide; used with diode-probe detector to measure guide wavelength, vswr and impedance. 1. C. Slotted line-probe tuner used as an impedance matching device. 1. D. Cavity wavemeter. Circular cross-section cavity wavemeter which resonates in the E011 mode and designed to measure frequency in the X-band range. 1. E. H-plane or shunt Tee waveguide junction; acts as a power divider in the plane containing the incident H (magnetic field). 1. F. Direction coupler: side-wall coupler type with directional coupling property, used to monitor power and measure vswr. 1. G. E-plane or series Tee waveguide junction; acts as a power divider in the plane containing the incident E (electric field). 56-200.

(10) Chapter 1 MICROWAVE TRAINER. Introduction and Description. Quantity. Identity No.. 1. H. Hybrid Tee, also known as a 'magic Tee', is a superposition of a shunt and a series Tee junction to form a 4-way junction; used to effect common transmitter/receiver antenna operation and in balanced mixer circuits. 2. J. Waveguide-to-coaxial transformer, used to interconnect waveguide to coaxial line and viceversa. 1. K. Resistive termination, a waveguide section containing a taper of lossy material to absorb incident microwave signals; ideally should absorb totally incoming signals without any reflection - it then acts as a matched load. 1. M. Diode detector in waveguide mount, used to rectify microwave signals for their detection; at low-power levels diode detector output current is directly proportional to the microwave power being detected.. 2. N. Horn antenna, an important microwave antenna widely used as a feed to microwave parabolic reflectors in radio, satellite and radar systems, and also as an antenna in its own right. 2. R. Short-circuit termination, metal plates used to shortcircuit waveguide section; employed in impedance measurements to determine reference planes, also used to measure guide wavelength and crystal detector law in conjunction with slotted line. 2. S. Probe detector, diode detector mounted in coaxial section with inner conductor acting as a probe; used in conjunction with slotted line and directional coupler to detect microwave signals [n.b. Letter S not marked on unit]. 1. 56-200. Description. Manual 56-200. 1-3.

(11) Chapter 1 MICROWAVE TRAINER. Quantity 1. Identity No.. Introduction and Description. Description Length of coaxial cable (approx. length 380 mm and external diameter 10 mm) with N-type connectors Accessories, contained in plastic bags: 2. coaxial cable (approx 3 mm external diameter) with BNC connectors for detector connection to console. 24 flange coupling clips for interconnecting waveguide components 4. 1-4. support plates. 56-200.

(12) Chapter 1 MICROWAVE TRAINER. Introduction and Description. Figure 1-1: Systems Components – Case Content. 56-200. 1-5.

(13) Chapter 1 MICROWAVE TRAINER. Introduction and Description. Notes. 1-6. 56-200.

(14) Chapter 2 MICROWAVE TRAINER. Assignments. 1 ASSIGNMENTS. 1.1 Introduction This chapter contains details of the practical assignments which can be undertaken using the microwave waveguide trainer. All assignments are essentially free-standing. They contain the information necessary for each assignments to be carried out on an individual basis. The numerical order follows a logical development, but assignments can be omitted or their order changed without loss in continuity or understanding. All assignments are essentially free-standing. They contain the information necessary for each assignments to be carried out on an individual basis. The numerical order follows a logical development, but assignments can be omitted or their order changed without loss in continuity or understanding. 1.2 List of Assignments 1. Introduction of a microwave waveguide bench and measurement of source frequency and wavelength.. 2. Measurement of voltage and standing wave ratio (VSWR).. 3. Measurement of diode detector law.. 4. Measurement of impedance and impedance matching.. 5. Horn antenna investigations.. 6. Use of a directional coupler in power transmission and reflected measurements.. 7. Series, shunt and hybrid T junctions.. 8. Waveguide to coaxial transformers.. 9. Microwave radio link investigations.. 56-200. 2-1.

(15) Chapter 2 MICROWAVE TRAINER. Assignments. Notes. 2-2. 56-200.

(16) Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. MICROWAVE TRAINER. CONTENT. In this first assignment a basic microwave measurement bench is set up to measure frequency and guide wavelength. The waveguide bench comprises a FET Dielectric Resonant Oscillator (DRO) source, two resistive vane attenuators, a cavity wavemeter, a waveguide slotted line, diode detectors and a resistive load termination. The frequency of the microwave source is measured using the cavity wavemeter. The guide wavelength lg is the wavelength of the microwave signal propagating in the waveguide. This is measured using a diode detector-probe unit to sample the standing waves set up in the slotted line when terminated in a short-circuit.. EQUIPMENT REQUIRED. 56-200. Quantity. Identifying letter. Component description. 1. ---. Control console. 2. A. Variable attenuators. 1. B. Slotted line. 1. D. Cavity wavemeter. 1. K. Resistive termination. 1. M. Diode detector. 1. P. X-band microwave source. 1. S. Probe detector assembly. 1. R. Short-circuit plate. 2-1-1.

(17) Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. MICROWAVE TRAINER. OBJECTIVES. When you have completed this assignment you should . Be familiar with some basic microwave waveguide components and know their use. . Know how to measure frequency using a cavity wavemeter. . Know how guide wavelength λg is measured using a slotted line. . Understand the meaning of cut-off wavelength and frequency. . Use the general relationship for waveguides of: 1 λ. 2 g. =. 1 λ. 2. -. 1 2. λc. to calculate guide wavelength, cut-off wavelength and free space wavelength and frequency.. KNOWLEDGE LEVEL. 2-1-2. No prior specialist knowledge is required to carry out this assignment. Basic concepts of waves, wavelength and frequency should be known. You should also be familiar with reading a micrometer. To assist in understanding the measurements taken in the assignment it would also be useful to appreciate . The nature of electromagnetic waves as being composed of oscillating electric and magnetic fields. . The action of a diode in rectifying alternating current and in microwaves in detecting microwave signals for measurement of field strength and power. . That waves in a closed environment can resonate, e.g. in a cavity when the cavity length is a whole number of halfwavelengths. . Certain types of waves, known as modes, can exist in waveguide structures and are characterised by their own particular wave pattern of electric and magnetic field. 56-200.

(18) MICROWAVE TRAINER. Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. INTRODUCTION (a) Measurement of source frequency using a cavity wavemeter Frequency in a microwave system can be measured using electronic counter techniques or by means of a cavity wavemeter.. Figure 2-1-1: Cavity Wavemeters. The principle of operation of the cavity wavemeter is based on the fact that very high Q-resonances can be obtained in metal waveguide cavities. Such cavities are usually of uniform circular or rectangular cross-section and resonate when their axial length equals an integral number of half guide wavelength, i.e. with reference to figure 2.1.1(a) when:. 1 L = n λg 2 where L = axial length of cavity n = 1,2,3...., the order of resonance λg = guide wavelength of resonating mode. 56-200. 2-1-3.

(19) Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. MICROWAVE TRAINER. Figure 2-1-1(b) illustrates a practical way of using a cavity as an absorption-type wavemeter. The cavity length L may be varied by altering the position of the short-circuit plunger. Off resonance the cavity absorbs little or no power from the main waveguide transmission system. However, at resonance considerable power is coupled into the cavity and this results in a corresponding dip observed in the main transmitted power. L at resonance can be very accurately determined. Knowing L, the type of resonant mode and the order of resonance enables the exciting frequency, the source frequency f, to be calculated. From theory: f=. c = 3 x 108 l.  1 1  2 + 2  lg lc .  n 2 1  = 3 x 108   + 2   2L  lc . where c = 3 x 108 m/s, the velocity of electromagnetic waves in free space lc = cut-off wavelength of mode resonant in the cavity n = order of resonance: n = 1, 2, 3..... More usually a calibration curve of frequency f versus L is provided. In high-quality wavemeters a cylindrical spiral scale measuring plunger position is calibrated to read frequency direct as illustrated in Figure 2-1-2.. Figure 2-1-2: Cavity Wavemeter Calibrated for Direct Reading Frequency. 2-1-4. 56-200.

(20) MICROWAVE TRAINER. Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. A diagram of the wavemeter used in the microwave trainer is sketched in Figure 2-1-3. The cavity consists of circular waveguide of diameter D = 28.3 mm. Its length can be adjusted to be a maximum of approximately 22 mm. Over the X-band frequency range the cavity can only support two modes, the H11 and the E01, whose cut-off wavelengths are given respectively by: H11 : lc = 1.71 D ; E01 : lc = 1.31 D so for the case of the wavemeter where D = 28.3 the values of cut-off wavelength and frequency are: H11 : lc = 48.4 mm , fc = 6.2 GHz E01 : lc = 37.1 mm , fc = 8.1 GHz. Figure 2-1-3: Cavity Wavemeter used in Microwave Trainer. A graph of resonant frequency versus micrometer reading for the wavemeter is plotted in Figure 2-1-4 for the first order resonant mode E011. The wavemeter used in the trainer is in fact designed to operate in the E011 mode. Thus if a dip is found in the transmitted power, see Figure 2-1-1(b), when the wavemeter micrometer is, for example, at 11.2 mm the frequency can be measured using the curve of Figure 2-1-4 and in this case would correspond to f = 10.4 GHz.. 56-200. 2-1-5.

(21) Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. MICROWAVE TRAINER. Cavity Wavemeter Calibration Curve 12.00. Frequency (GHz). 11.50. 11.00. 10.50. 10.00. 9.50 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Micrometer Scale (mm). Figure 2-1-4: Calibration Curves for Cavity Wavemeter. Diameter D = 28.3 mm. Note 0.00 point of micrometer scale corresponds to cavity length of 11.63 mm and this offset is taken into account in the above graph.. 2-1-6. 56-200.

(22) MICROWAVE TRAINER. (b) Guide wavelength and its measurement. Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. Free space wavelength l is the distance travelled by the wavefront of the electromagnetic wave in free space in the duration of one cycle. It is related to frequency f by: 8. fλ = c , c = 3 × 10 m / s c λ= f. When the waves are guided by a waveguide they travel in the form of distinctive wave patterns known as modes and the wavelength of the guided transmission is known as the guide wavelength λg. For rectangular and circular waveguides, λg is related to l by the formulae: 1 2 g. λ. =. λg =. 1 2. λ. =. 1. (2). 2. λc. λλ c. (λ. 2 c. 2 0. −λ. ). (3). where λc = the cut-off wavelength of the mode propagating . For the case of rectangular waveguides, transmission is invariably limited to single-moded operation in its dominant H10 mode. The cut-off wavelength for the H10 mode is: λc = 2a. where a = internal broadside dimension of the waveguide. Thus if f is known, λ can be determined and λg can be calculated for a given size of waveguide using formula 3. The guide wavelength can be measured experimentally using the slotted waveguide section and probe-detector components shown diagrammatically in Figure 2-1-5. By terminating the slotted section in a short circuit a standing wave pattern can be set up. The incident wave from the source and the reflected wave from the short-circuit combine to give a resultant standing wave in the section whose electric field amplitude varies as shown in Figure 2-1-6 The distance between successive nulls is in the standing wave ½λg and can be measured very accurately. Thus guide wavelength can be determined experimentally to a high degree of accuracy. 56-200. 2-1-7.

(23) MICROWAVE TRAINER. Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. Figure 2-1-5. Diagrammatic sketch indicating main components of a waveguide slotted line and diode-probe detector for investigating standing waves in rectangular waveguide.. Figure 2-1-6. Standing wave electric field pattern on a short-circuited line; distance between successive null =1/2 λg. 2-1-8. 56-200.

(24) MICROWAVE TRAINER. Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. EXPERIMENT PROCEDURE WARNING:. Although the microwave power levels generated by the equipment are below 10 mW and not normally dangerous, the human eye can suffer damage exposed to direct microwave radiation. Therefore: NEVER look directly into an energised waveguide.. (a) Measurement of frequency using a cavity wavemeter. Figure 2-1-7 1.. Set up the microwave components as shown in Figure 2.1.7 with the switch positions on the control console initially as follows: main green power switch : off; amplifier and detector sensitivity control knob : to mid-position;. 56-200. 2-1-9.

(25) MICROWAVE TRAINER. Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. supply for X-band oscillator : left-hand switch : switch to internal keying; right-hand switch : off 2.. Make sure the coaxial cables are also in place to connect the power supply for the X-band oscillator and to connect the diode detector output to the amplifier and detector input on the console.. 3.. Set the micrometer position of the cavity wavemeter fully out to a reading greater than 15 mm. In this position, the short-circuit plunger terminating the far end of the cavity is also fully out and the cavity is at its maximum length.. 4.. Set the angular position of the resistive vane for both attenuators at about 20°. At these settings, the attenuators reduce the microwave power in the bench by the order of 10 dB and avoid possible diode-detector and display meter overload when we switch on.. 5.. Now switch on the main green power switch and the right-hand supply switch for the X-band oscillator to energise the bench.. 6.. Adjust the attenuator adjacent to the diode detector to give a meter reading on the console meter of about 4 mA. Note increasing the vane penetration reduces the microwave power transmitted in the system.. 7.. Determination of frequency using the wavemeter. Turn the micrometer thimble of the wavemeter very slowly clockwise to move the short-circuit plunger downwards and thus reduce the length of the cavity. Observe the meter deflection whilst this is being done. Search for a position at which there is a sharp dip in the meter reading. Such a dip corresponds to a resonance at which power is absorbed by the wavemeter and so reduces the transmitted microwave power as detected by the diode-detector and observed on the meter. Record the micrometer reading at this resonance and determine the frequency of the microwave signals using the E011 mode calibration curve of Figure 2-1-4.. 2-1-10. 56-200.

(26) Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. MICROWAVE TRAINER. NOTE. (i). The linear scale on the micrometer barrel of the wavemeter is graduated in 0.5 mm intervals. The circular scale on the thimble is graduated 0 to 50 with each graduation representing a 0.01 mm movement. Thus the vertical movement of the short-circuit and hence the cavity length and resonance position can be measured extremely accurately.. (ii). The design of the wavemeter is such that it resonates principally in the E011 mode and hence the curve for this mode should be used in Figure 2-1-4.. (iii). At micrometer readings of the order of 5 mm and below a number of deep over-lapping resonances may also be observed. These are termed "spurious" and should be ignored. They arise principally to leakage of energy past the plunger.. (b) Measurement of guide wavelength, λg. Figure 2-1-8. 56-200. 2-1-11.

(27) MICROWAVE TRAINER. Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. 1.. The guide wavelength is measured using the waveguide slotted line component B fitted with one of the diode-detector/probe units S. This unit should be mounted so that its probe penetrates a short distance into the slot thereby allowing the electric field to be sampled. The depth of penetration is a compromise between obtaining reasonable coupling for the probe-detector to provide an observable meter reading without the probe causing undue disturbance of the field in the waveguide and thus invalidate the measurements. In practice a penetration depth of 1 to 2 mm should suffice.. 2.. Connect the equipment as shown in Figure 2-1-8 with the slotted waveguide section terminated in the metal plate R acting as a short-circuit.. 3.. Set the switch positions on the control console as follows: green power switch : off; left-hand switch of supply for X-band oscillator : to internal keying; right-hand oscillator switch : off. Check also the coaxial cables are correctly connected : oscillator output cable on console to microwave source; probe-detector unit cable to input of amplifier-detector on the console.. 4.. Now switch on power and oscillator and adjust attenuators and if necessary the sensitivity control on the console to obtain a detector reading. Move the probe to locate a position of maximum field and re-adjust sensitivity control and/or attenuators to provide a meter reading close to full scale, say 4 mA.. 5.. Starting from zero on the slotted-line scale move the probe along the slotted waveguide section and locate and record the positions of electric field nulls. It should be possible to locate 3 consecutive nulls: x1 = x2 = x3 =. 2-1-12. 56-200.

(28) MICROWAVE TRAINER. Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. The guide wavelength: λg = 2 (x2 - x1) =. = 2 (x3 - x2) = = (x3 - x1) 6.. =. The waveguide used in the Microwave Trainer is standard WG16 whose internal dimensions are broad dimension. a = 0.9 inch = 22.86 mm. narrow dimension. b = 0.4 inch = 10.16 mm. The cut-off wavelength for the dominant mode, the H10 mode is λc = 2a. = 2 x 22.86 mm = 45.72 mm for WG 16 Using the result of formula (3) and the above value of λc determine the guide wavelength λg at the source frequency, f = 10.7 GHz. Compare with the experimentally determined value. SUMMARY. 56-200. In this assignment two important parameters have been measured and a number of basic microwave components have been used. Frequency has been measured using a cavity wavemeter and guide wavelength has been measured experimentally using a waveguide slotted line. The relationship between free space wavelength l has also been introduced and used to determine guide wavelength.. 2-1-13.

(29) MICROWAVE TRAINER. Assignment 1 Introduction of a Microwave Waveguide Bench and Measurement of Source Frequency and Wavelength. Notes. 2-1-14. 56-200.

(30) Assignment 1 MICROWAVE TRAINER. (a). Typical Results and Answers. Measurement of frequency using the cavity wavemeter. Starting with the micrometer withdrawn to maximum length a sharp resonance is observed at a micrometer reading of 11.17 mm. Using calibration curve of Figure 2-1-4 for the E011 mode frequency f = 10.42 GHz. Alternatively using the formula:  1 1 f = c  2 + 2   4L λc . 1.. with. 1 2. c = 3 x 108 m/s L = 11.17 + 11.63 mm = 22.8 mm (11.63 mm to correct micrometer scale to read total cavity length) λc = 37.1 mm for the E01 mode. we have f = 3 x 108 (1/4 x 0.0232 + 1/0.03712)½ = 3 x 108 (484 + 727)½ = 10.42 GHz. Note:. At much lower micrometer readings, typically below 5 mm, a number of deep overlapping resonances may be observed. These carry no useful information and should be ignored; they arise due to limitations in the wavemeter design, notable leakage around the short-circuit plunger.. 56-200. 2-1-15.

(31) Assignment 1 MICROWAVE TRAINER. (b). Typical Results and Answers. Measurement of guide wavelength, lg. With the slotted line section terminated in a short-circuit nulls are observed at scale positions x1 = 27 mm so. x2 = 45.4 mm x3 = 64 mm. X2 - x1 = 18.4 mm. , lg = 2 x 18.4 = 36.8 mm. x3 - x2 = 18.6 mm. , lg = 2 x 18.6 = 37.2 mm. x3 - x1 = 37 mm. , lg = 37 mm Average = 37 mm. Check using formula (3): 2.. λg =. λ λc. (λ. 2 c. - λ2. ). The waveguide size of the guide used in the trainer is WG16 with a = 0.9 inch = 22.86 mm so for the H10 mode, λ = 2a = 45.72 mm and at the measured frequency of f = 10.42 GHz, 3.. λ=. c 3 x 108 = = 28.76 mm f 10.42 x 109. we have: 4.. lg =. 28.76 x 45.7. (45. 7. 2. - 28.762 ). = 37 mm. showing very good agreement with the measured value.. 2-1-16. 56-200.

(32) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER CONTENT. EQUIPMENT REQUIRED. OBJECTIVES. In this assignment, the measurement of voltage standing wave ratio (VSWR) of waveguide components is undertaken using a waveguide slotted-line and probe detector. Voltage standing wave ratio, invariably abbreviated to VSWR, is one of the fundamental parameters used in specifying component performance. It quantifies the degree of mismatch a component presents to the waveguide feed line. Quantity. Identifying letter. Component description. 1. ---. Control console. 2. A. Variable attenuators. 1. B. Slotted line. 1. S. Probe-diode detector. 1. P. X-band source. 1. K. Resistive termination. 1. N. Waveguide horn. When you have completed this assignment you should: ! Know the definition of voltage standing wave ratio and its relation to reflection coefficient ! Know how to measure VSWR using a slotted line and probe-detector ! Know the method used to measure high values of VSWR. KNOWLEDGE LEVEL. 56-200. No prior specialist knowledge is required to carry out this experiment, although completion of Assignment 1 would be a distinct advantage.. 2-2-1.

(33) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER INTRODUCTION. When a component is connected into a transmission line system it will cause reflection at the junction between the line and the component unless it is correctly matched or a matching unit is used. The reflected wave from the component and incident wave from the source set up a standing wave pattern in the feed line as illustrated in Figure 2-2-1. Figure 2-2-1: Standing Wave Pattern: VSWR S = Vmax/Vmin or Emax/Emin. Standing waves cause undesirable effects. They can give rise to very high values of voltage/electric field strength in the waveguide and this can cause breakdown in high-power systems. Reflection caused through the mismatch between the line and component reduces the amount of power that can be transferred below optimum and can adversely affect the efficiency of a communications or radar system. Power can be wasted in a transmitter by being reflected, for example, at the antenna input. Likewise, power can be lost by mismatch reflection at an antenna-receiver station. The voltage standing ratio, vswr, is universally used to quantify the degree of mismatch. It is denoted by the letter S and defined as: S =. Vmax E = max Vmin Emin. where Vmax, Emax = voltage or electric field strength at a position of field maximum. Vmin, Emin = voltage or electric field strength at a position of field minimum. 2-2-2. 56-200.

(34) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER. There is an important relation between vswr, S, and reflection coefficient G: G = Vr/Vi where. Vi = incident wave voltage or electric field amplitude Vr = reflected wave amplitude. and since. Vmax = Vi + Vr = Vi (1 + G) Vmin = Vi - Vr = Vi (1 - G) S =. 1+ Γ Vmax = 1- Γ Vmin. Γ =. S- 1 S+ 1. The table below provides a useful guide to the relationships of VSWR, reflection coefficient G and power reflected due to mismatch. vswr S. Reflection coefficient Γ. % power reflected 2 Γ %. 1.0. 0. 0. System matched. 1.05. 0.048. 0.22. Very good match. 1.5. 0.2. 4.0. Fair, just acceptable. 2.0. 0.33. 11.1. Poor match, not usually acceptable. 5.0. 0.67. 44.4. Reject, faulty, unacceptable. Comment. The voltage standing wave ratio produced by a waveguide component may be measured using a slotted waveguide section and a diode detector probe. The slotted section is inserted in the waveguide system to provide a means of sampling the standing wave electric field pattern produced by reflection from the component under consideration. The slotted section consists of waveguide with a narrow axial slot cut in the centre of its broad face as indicated in Figure 2-2-2(a). A narrow slot in this position is non-radiating and causes negligible distortion to the waves within the waveguide. Coupling to the electric field is made by a 56-200. 2-2-3.

(35) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER. probe which penetrates a small distance through the slot as illustrated in Figure 2-2-2(b). The probe is connected in series with a crystal diode detector and the unit contained in a carriage that may be moved along the slot so enabling the field at different axial positions to be measured. The diode detector rectifies the sampled microwave signal and the rectified current is measured on a DC milliammeter.. Figure 2-2-2: Slotted Waveguide and Diode Detector Probe Unit for Measuring Voltage Standing Wave Ratio. For small currents the diode-detector obeys a square law such that the detected current is proportional to the square of the electric field induced in the probe. Thus, if the values of maximum and. VSWR, S = E max E min minimum current are measured, we have:. so S =. Emax = Emin. Imax Imin. =. Imax Imin. where Ιmax = current measured at field maximum E. 2 max. where Ιmax = current measured at field maximum E. 2 min. for small current conditions 2-2-4. 56-200.

(36) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER. e.g. if Ιmax is measured at 4.6 mA and Ιmin at 3.2 mA S =. Emax = EMIN. 4.6 = 3.2. 1.44 = 1.2. Voltage standing wave ratio can be measured without knowledge of the diode-detector characteristics by using a precision attenuator. The probe is moved to a position of minimum and the value of the attenuator attenuation A1 dB noted which gives a convenient current reading on the meter for reference. The probe is then moved to locate a position of maximum and the attenuator adjusted to provide the same reading as obtained with the minimum. Suppose the new attenuation value is to be A2, then: attenuation added = A2 – A1 2 2 max/E min). = 10 log (E. = 20 log (Emax/Emin) = 20 log S (A2 – A1)/20. so S =antilog10 (A2 – A1)/20 or 10. For large values of vswr, typically S > 3, Emin and therefore the detector current will become very small and the ratio Emax to Emin increasingly difficult to measure accurately. For these cases a method based on locating the minimum and determining the distance between points either side of the minimum at which the field is a constant factor, k say, times the minimum value. With reference to Figure 2-2-3 and assuming a square law for the diode detector, the VSWR may be evaluated from the formula. S =. [k. 2. - cos2 ( π d/ λ g). ].  π d sin    λ g where d = distance between points where electric field, E = k Emin 2. detector current, I = k Imin lg = guide wavelength 56-200. 2-2-5.

(37) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER 2. k = I/Imin 2. It is common practise to choose k = 2 so d = distance between points where detector current equals 2 Imin and in this case the formula for S reduces to. S = 1+. 1  πd  sin2    λg . Figure 2-2-3: Plotting around the Field Minimum Method for Measuring High Values of VSWR. e.g.. if d = 1.5 mm and lg = 35.5 mm pd/lg = 0.133 rad or 7.61°. so:. S =. 2-2-6. 1   2  1+  = sin 7.61 . [ 1+. 57.1. ]. = 7.6. 56-200.

(38) MICROWAVE TRAINER. Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). EXPERIMENTAL PROCEDURE WARNING: Never look into an open-ended waveguide system. Microwave radiation can cause harm. 1.. Set up the equipment as shown in Figure 2.2.4 with the resistive termination component connected to the slotted line section. The depth of penetration of the probe of the diode detector into the slotted line should be set at approximately 1 to 2 mm. Our first task is to measure the VSWR of the resistive termination component.. Figure 2-2-4: Experiment set up to Measure VSWR Resistive Load. 56-200. 2-2-7.

(39) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER 2.. Set the switch conditions on the console as follows: amplifier and detector: switch to detector output amplifier and detector sensitivity control: turn to mid-position supply for X-band oscillator: left-hand keying switch: switch to internal keying right-hand switch: initially off Now switch on the console power supply, the main green switch, and energise the microwave bench by switching the right-hand Xband oscillator switch on. 3.. Set the attenuator at about 25° to provide a reasonable level or attenuation in the system. This is good practice since attenuation between the microwave oscillator and the equipment it drives helps reduce detuning of the oscillator due to reflected signals. Move the probe-detector unit along the slotted line to locate a position of electric field maximum. Adjust the detector sensitivity of the amplifier and detector on the console and, if necessary, the attenuator setting to obtain a meter reading close to full-scale deflection. Record the detector current Imax corresponding to Emax.. 4.. Now move the probe-detector unit away from the maximum and locate accurately the position of the adjacent minimum. Record the detector current Imin corresponding to Emin.. 5.. Using the results: Imax =. Imin =. Calculate for the resistive load termination: the VSWR S =. E max = E min. I max = I min. the reflected coefficient, | Γ| =. 2-2-8. S- 1 = S+ 1. 56-200.

(40) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER the % of power reflected,. 100| Γ |2 =. %. the return loss, 10 log. Pr = 20 log | Γ| = Pi. dB. where Pr, Pi = reflected and incident powers, respectively 6.. Measurement of VSWR for the horn antennas Remove the resistive load termination and connect one of the horn antennas. Measure its VSWR by measuring Imax and Imin as described in steps 2 and 3. Repeat with the second horn. Results and calculation of VSWR Horn 1. Horn 2. Imax =. Imax =. Imin =. Imin =. VSWR =. 7.. Imax = Imin. VSWR =. Imax = Imin. Measurement of larger values of VSWR: plotting around the minimum method The horn antenna presents a very good match to the waveguide and hence has a VSWR quite close to unity. A component with a higher value of VSWR can be simulated by using the second attenuator terminated by a short-circuit plate. (i). 56-200. Remove the horn and connect the attenuator terminated in a short circuit as shown in Figure 2-2-5.. 2-2-9.

(41) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER. Figure 2-2-5. (ii). Set the attenuator to 40° which provides a fairly low attenuation value (typically 2 to 3 dB).. (iii) Move the probe-detector along the slotted line section to locate an electric field minimum. Note the detector meter reading Imin. (iv) Next move the probe-detector to the right until the detector meter registers twice the minimum current value, i.e. 2 Imin 2 (corresponding to k = 2). Record the probe-detector position on the slotted line scale, x1 say. (v). 2-2-10. Now move the detector probe to the left through the minimum and locate the position where the detector meter current is again 2 Imin. Record the probe-detector position, x2.. 56-200.

(42) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER. (vi) Measure the guide wavelength by finding the distance between successive minima and remembering: distance between successive minima = ½ lg (vii) Results and calculation of VSWR position where I = 2 Imin :. x1. =. x2. =. d. = x1 - x2. lg = 2 x distance between minima = VSWR S = 1 +. SUMMARY. 1  π d 2  sin   λg . The VSWR of waveguide components has been measured using a waveguide slotted line to measure the ratio of maximum to minimum electric fields produced in the standing wave pattern set up by the components. Components with a VSWR close to 1 have very low reflection coefficient and present a good match to their waveguide feed. A method for the measurement of large values of VSWR based on determining the relative width about an electric field minimum has also been undertaken. Both methods assumed a square law for the diode detector. Measurements of VSWR independent of the diode detector characteristics may be made by measuring the ratio Emax/Emin using a precision attenuator.. 56-200. 2-2-11.

(43) Assignment 2 Measurement of Voltage and Standing Wave Ratio (VSWR). MICROWAVE TRAINER Notes. 2-2-12. 56-200.

(44) Assignment 2 MICROWAVE TRAINER. Typical Results and Answers. Resistive load Imax = 4 8 mA Imin = 2.4 mA vswr S =. 4.8 Imax = = 1.41 2.4 Imin. Note this result indicates that the resistive load presents a rather poor match with:. reflection coefficien t, | Γ | =. S - 1 1.41 - 1 = 0.17 = S + 1 1.41 + 1. 2. % power reflected, | Γ | x 100 = 3%. Horn antenna. Both horns gave very similar results: Imax = 4.2 mA Imin = 3.0 mA. so vswr S =. 4.2 = 1.4 = 1.18 3.0 | Γ | = 0.08. % power reflected = 0.68% showing the horns present an excellent match. 56-200. 2-2-13.

(45) Assignment 2 MICROWAVE TRAINER Attenuator terminated in short circuit. Typical Results and Answers. Attenuator setting 40° Imin = 0.6 mA. position at I = 2 Imin = 1.2 mA x1. = 41.8 mm. x2. = 45.0 mm. d. = x1 - x2 = 45 – 41.8 = 3.2 mm. λg. = 36.5 mm. so. πd λg. =. π 3.2 = 0.088 π rad or 15.8° 36.5. 1   hence S =  1 + = 2 sin 15.8°  . 2-2-14. [ 1 + 13.4 ] = 3.8. 56-200.

(46) Assignment 3 MICROWAVE TRAINER. CONTENT. EQUIPMENT REQUIRED. OBJECTIVES. Measurement of Diode Detector Law. The characteristic of rectified current versus microwave power for a diode crystal detector is investigated at low-power levels. The validity of the diode detector "square -law" whereby the rectified current output is directly proportional to incident microwave power (itself proportional to the square of the electric field amplitude) is tested. Quantity. Identifying letter. Component description. 1. ---. Control console. 1. A. Variable attenuator. 1. B. Waveguide slotted line. 1. S. Probe diode-detector assembly. 1. P. X-band microwave source. 1. R. Short circuit plate. When you have completed this assignment you will Appreciate the use of a crystal diode as a sensitive detector of microwave signals Know that at low signal levels (typically in the microwatt range) that the rectified output is directly proportional to the square of the electric field and hence the microwave power flowing in the waveguide Know how the 'square law' may be tested experimentally Gain further experience of standing waves and the use of waveguide components. KNOWLEDGE LEVEL. 56-200. No prior knowledge is required to carry out this assignment, although it is strongly recommended that assignments 1 and 2 have already been completed.. 2-3-1.

(47) Assignment 3 MICROWAVE TRAINER. INTRODUCTION. Measurement of Diode Detector Law. Diode crystal detectors are widely used as a detector of microwave signals at low power levels. The action of the diode and two basic detector circuits are indicated in Figure 2-3-1.. Figure 2-3-1: Diode Detector - Action and Basic Circuits. For power level up to about 10 microwatts the crystal detector has a square law characteristic, that is, the detector voltage or current output is directly proportional to the square of the electric field, which in turn implies that the diode detector output is proportional to the power of the microwave signal. The low-level sensitivity of a good quality diode detector is of the order 0.5 millivolts per microwatt. At higher power levels the crystal detector deviates from the square law becoming an approximate linear 2-3-2. 56-200.

(48) Assignment 3 MICROWAVE TRAINER. Measurement of Diode Detector Law detector at levels of the order of 0.1 milliwatts. Over the linear part of the characteristic the rectified output is directly proportional to the microwave electric field strength. In this experiment, the diode-detector characteristic is investigated at low-power levels using a slotted waveguide and a probe diode detector unit (see Assignment 2, Figure 2-2-2). The detector current is measured for the known variation of electric field strength present in the slotted waveguide section when this section is terminated in a short-circuit. The magnitude of electric field strength in a short-circuited line, see Figure 2-3-2, is given by E = 2Ei sin bl where Ei = incident field amplitude l = distance from short-circuit b = 2p/lg. Figure 2-3-2: Variation of Electric Field Amplitude in the Standing Wave Pattern of a Short-Circuited Line. If we assume the average diode detector rectified current as measured by the meter is related to field strength by the relationship I = k En 56-200. 2-3-3.

(49) Assignment 3 MICROWAVE TRAINER. Measurement of Diode Detector Law where n = 'crystal law', then we have for the case of a shortcircuited line: I = k (2Ei sin bl)n so if we were to plot log I (y - axis) versus log (sin bl), the graph should be a straight line and the gradient or slope of this line gives n, the crystal law power. For low-power levels we should establish that n = 2 showing the square-law relationship is valid.. EXPERIMENTAL PROCEDURE WARNING: Never look into an open-ended waveguide system. Microwave radiation can cause harm. Figure 2-3-3. 2-3-4. 56-200.

(50) Assignment 3 MICROWAVE TRAINER. 1.. Measurement of Diode Detector Law. Set up the equipment as shown in Figure 2-3-3 with the slotted waveguide section terminated in a short-circuit plate and the variable attenuator set initially at 0°, its maximum attenuation setting. The depth of penetration of the probe of the diode detector should be set at approximately 1 to 2 mm. This ensures that the field in the slotted section is not unduly disturbed by the probe but still provides a low-level but measurable input to the diode detector.. 2.. Set the switches on the console as follows: left-hand keying switch: switch to internal keying right-hand switch: initially off Now switch on the console supply (main green switch on) and energise the microwave oscillator by switching the right-hand switch on.. 3.. Gradually reduce the attenuation in the attenuator by moving the resistive vane from the 0° position until a deflection is observed on the meter. Move the probe unit along the slotted waveguide section and locate a position of maximum as indicated by maximum detector current reading. This position corresponds to a maximum of electric field produced by the standing wave pattern set up in the slotted waveguide section by the incident wave and the wave reflected at the shortcircuit termination. Now adjust the attenuator and, if necessary, the detectoramplifier sensitivity control to provide a meter reading of this maximum close to full scale deflection.. 56-200. 2-3-5.

(51) Assignment 3 MICROWAVE TRAINER. 4.. Measurement of Diode Detector Law. Next, move the probe along the slotted waveguide and locate accurately the position of an electric field null. At the position of a null the detector current is virtually zero. Working from this point as reference and away from the short-circuit end of the slotted line, take a series of detector current readings at a number of points up to the position of a field maximum. Record the results in a table similar to that given below. Probe position as measured on slotted-section scale - L mm. Probe position relative to electric field null l = L - Lo. At null, E = L1 = L0 =. 5.. I mA E= I=0. l=0. Measure the guide wavelength lg by determining the distance between successive nulls. It should be possible to measure the positions of 3 successive nulls; first null position, L1. =. second null position, L2. =. third null position, L3. =. then lg = 2(L2 - L1). =. = 2(L3 - L2). =. =. 2-3-6. Diode detector current. L3 - L1. =. 56-200.

(52) Assignment 3 MICROWAVE TRAINER 6.. Measurement of Diode Detector Law Calculate the values of log I and log (sin bl) tabulating your results in a table similar to that given below. Distance l. bl = 2pl/lg = 360 l/lg°. sin bl. log (sin bl). Detector current I mA. log I. 0. 0. 0. ---. 0. ---. 7.. Plot the graph of log I versus log (sin bl) and draw in the "best-fit" straight line. Measure the gradient of this line and hence deduce the diodedetector law, the value of n. This should be approximately 2.. 56-200. 2-3-7.

(53) Assignment 3 MICROWAVE TRAINER. SUMMARY. Measurement of Diode Detector Law. Diode crystal detectors are very widely used for low-level microwave signal detection. They are extremely sensitive devices and at very low power levels up to about 10 micro-watts they obey a square law, i.e. detector output current (or voltage) is directly proportional to the square of electric field; equivalently detector output is directly proportional to microwave power. In this experiment a known field variation in a waveguide is set up by short-circuiting a length of slotted line. This field was sampled using a probe-diode detector unit. The RF field picked up by the probe was rectified by a crystal diode and measured at a number of points between positions of minimum and maximum as the probe unit was moved along the slot of the waveguide section. Results were used to plot a graph and test the validity of the square law condition: detector output I ∝ E2 (electric field squared) ∝ PRF (microwave power). 2-3-8. 56-200.

(54) Assignment 3 MICROWAVE TRAINER. SPECIMEN RESULTS. Typical Results and Answers. Guide wavelength measured at, lg = 37.1 mm. l mm. 360 l/lg°. sin bl. log (sin bl). I mA. log I. 0. 0°. 0. ---. 0. ---. 1.0. 9.7. 0.169. –0.78. 0.2. –0.7. 2.0. 19.4. 0.332. –0.48. 0.65. –0.19. 3.0. 29.1. 0.486. –0.31. 1.7. +0.23. 4.0. 38.8. 0.628. –0.20. 2.65. +0.42. 5.0. 48.5. 0.749. –0.13. 3.5. +0.54. 6.0. 58.2. 0.850. –0.07. 4.05. +0.60. 7.0. 67.2. 0.927. –0.03. 4.45. +0.65. 8.0. 77.6. 0.977. –0.01. 4.95. +0.70. 9.0. 87.3. 0.999. –0.005. 5.15. +0.71. 56-200. 2-3-9.

(55) Assignment 3 MICROWAVE TRAINER. Typical Results and Answers. The graph of log I versus log (sin bl) is plotted below in graph 2-34 and a 'best-fit' line drawn. The gradient or slope of this line gives n = 1.86, a fair approximation to the square-law relationship.. Figure 2-3-4: Graph of Log I versus Log sin βl. gradient n =. 2-3-10. Y 1.3 = ≅ 1.86 X 0.7. 56-200.

(56) Assignment 4 MICROWAVE TRAINER CONTENT. EQUIPMENT REQUIRED. OBJECTIVES. KNOWLEDGE LEVEL. 56-200. Measurement of Impedance and Impedance Matching The concept of impedance in waveguides and the use of the Smith Chart in impedance and matching calculations are introduced. The measurement of impedance of a waveguide component is carried out and the results used to determine the position of a capacitative probe to effect matching. Quantity. Identifying letter. Component description. 1. ---. Control console. 1. A. Variable attenuator. 1. B. Waveguide slotted line. 1. C. Slotted line probe tuner. 1. K. Resistive termination. 1. P. X-band oscillator source. 1. S. Probe-diode detector used with slotted line. 1. R. Short-circuit plate. When you have completed this assignment you . Should understand the terms normalised impedance and admittance of a waveguide component. . Know how to measure normalised impedance by measuring the vswr and position of a electric field or voltage minimum in the standing wave pattern produced by the component. . Appreciate the use of the Smith Chart in aiding impedance determination. . Appreciate the need for matching. . Know how matching can be accomplished using a slotted line probe/screw tuner. Before you commence this assignment you . Should look at Assignment 2 and know the significance of vswr and how it can be measured. . Appreciate that a load terminating a waveguide or a transmission line will cause reflection and produce a standing wave unless matched. 2-4-1.

(57) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching . Be familiar with the basic results of transmission line theory. INTRODUCTION. Summary of basic transmission line and standing wave results of a terminated line. (1). Input impedance normalised impedances and reflection coefficient of a terminated line The impedance of a waveguide load is determined using the general result for the impedance of a terminated line given by transmission line theory. Since voltage and current cannot be measured in a waveguide, the actual measurement of impedance is deduced from the standing wave electric field pattern set up by the load. From transmission line theory, we have for the input impedance of a line of characteristic impedance Z0 when terminated in a load of impedance, ZT, as indicate in Figure 2-4-1. Zin (l) =. V(l) Z + j Z0 tanβ l = Z0 T I(l) Z0 + j ZT tanβ l. (1). where l = line length β = 2π/lg, the phase constant of the line lg = guide wavelength. Figure 2-4-1. The result given by (1) is general and can be used to quantify waveguide loads as impedances in much the same way as impedances are used at lower frequencies and in coaxial and parallel wire type lines. In these types of lines voltage and current can be defined and their characteristic impedance uniquely determined. Typical Z0 values for coaxial lines used in RF work are 50 Ω and 75 Ω. 2-4-2. 56-200.

(58) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching The characteristic impedance of waveguides, however, cannot be uniquely specified and so to avoid this difficulty impedance levels are relative to Z0 as normalised impedances. zin (l) =. Zin (l) Z0. =. Z T + jZ0 tan β l Z0 + jZ T tan β l. =. Z T / Z0 = j tan β l 1 + jZ T / Z 0 tan β l. =. zT + j tan β l 1 + jzT tan β l. (2). where zT = ZT/Z0 = normalised load impedance. The reflection coefficient at the load is given by: Γ =. =. Z T - Z0 Z T + Z0 zT - 1 zT + 1. (3). so unless ZT = Z0 or equivalently ZT = 1 reflection will occur. If the load is matched to the line, that is ZT = Z0, then G = 0 and no reflection occurs. (2). Admittance As well as working in impedances it will be also convenient to work in admittances. This is especially so in matching applications where shunt elements are employed (elements connected in parallel).. 56-200. 2-4-3.

(59) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching. Admittance is the reciprocal of impedance and so formulae (1), (2) and (3) can be expressed in terms of admittance as Yin (l) =. I(l) YT + jY 0 tan βl = Y0 V(l) Y0 + jY T tan βl y T + j tan βl 1 + jy T tan βl. (21). Y0 - Y T 1 - yT = Y0 + YT 1 + yT. (31). yin (l) =. Γ=. 2.. (11). Measurement of normalised impedance of a waveguide load. Figure 2-4-2. Figure 2-4-2 illustrates a typical standing wave pattern set up by a load terminating a line when a mismatch between line and load occurs. The plot of electric field amplitude versus distance from the load shows a variation between points of maximum Emax and minimum Emin. By measuring the voltage standing wave ratio, the VSWR, S, and the position of the first minimum, d, from the load, the normalised load impedance ZT can be determined.. 2-4-4. 56-200.

(60) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching. At a voltage or electric field minimum, the incident and reflected waves are in anti-phase and the normalised input impedance of the line at this point is resistive and equal to 1/S. Thus: when l = d. zin (d) =. 1 zT + j tan βd = s 1 + jzT tan βd. where. Emax Emin. , the VSWR. and. S=. (3). d = distance from load of first E - field minimum. We solve (3) for the normalised load impedance: ZT =. 1 - jS tan β d S - j tan β d. and expressing zT in terms of its real and imaginary parts, we have real or resistive part of zT ,. rT =. imaginary or reactive part of zT ,. S ( 1 + tan2 β d) 2 2 S + tan β d. xT. =. (1 - S2) tan β d 12 2 S + tan β d. (4). (5). In the practical experiment the vswr is measured by measuring the detector current Imax at a maximum and at a minimum Imin using the slotted line: S = Emax = Imax Emin Imin. The distance, d, is best measured by recording the positions of minimum with load and short-circuit terminations, then with reference to Figure 2-4-2 d = xmin (load) - xmin (short-circuit) The calculations to determine zT expressed by the formulae (4) and (5) can be accomplished by use of a calculator or with the aid of a Smith Chart. The procedure using a Smith Chart is explained in the Typical Results section at the end of this assignment. 56-200. 2-4-5.

(61) Assignment 4 MICROWAVE TRAINER 3.. Measurement of Impedance and Impedance Matching Matching a load using a reactive stub The slotted line probe tuner, component C, shown in Figure 2-43, acts as a shunt reactance element and is a useful component in effecting matching. For small penetrations of the probe, capacitative susceptance can be introduced which increases the penetration, but eventually changes sign and becomes inductive. In most matching applications, units of this type consist of either a probe, post or screw and are inserted to produce capacitative susceptance.. Figure 2-4-3 Slotted Line Probe Tuner. The principle of shunt stub matching may be explained with reference to Figure 2-4-4(a). We look for a point at a distance from the load where the real part of the input admittance is unity, i.e. where: yin (l) = 1 ±jb Then if at this point we connect in a shunt stub of susceptance equal in magnitude but opposite in sign we can cancel out the load susceptance so that yin = 1 and thus effect matching to the feed line.. 2-4-6. 56-200.

(62) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching. Figure 2-4-4 Shunt Stub Matching. We can locate the position where yin(l) = ±jb by finding the position d of the first electric field minimum and then using the known admittance at this point as a new load: yT = S at a minimum in the general formula for transmission line input admittance. We solve this for the condition that the real part of yin = 1, i.e: yin (lm) =. y T + j tan βlm where yT = S 1 + jy T tan βlm. solving for the real part of yin and equating to unity, we obtain the condition: tan2 βlm = l/S so. lm =. ±λg 1 tan–1 (l/S) = = tan–1 (l/S) 2π β. We have in fact two values, one positive and one negative, for lm, so there are two positions either side of the voltage minimum position satisfying real [yin] = 1. The negative value of lm corresponds to yin = 1 + jb and would require inductive susceptance for matching, the positive value used in this assignment requires capacitative susceptance as yin = 1 – jb.. 56-200. 2-4-7.

(63) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching. EXPERIMENTAL PROCEDURE WARNING: Microwave radiation can be harmful, especially to eyes. NEVER look into energised waveguide.. Measurement of the normalised impedance of a waveguide. Figure 2-4-5. 2-4-8. 56-200.

(64) Assignment 4 MICROWAVE TRAINER. 1.. Measurement of Impedance and Impedance Matching. Set up the equipment as shown in Figure 2-4-5. The waveguide load whose impedance we are to measure is connected to the slotted line section. Our test load in this experiment is the resistive termination, component K. Note: The probe of the probe-detector S mounted on slotted line should be adjusted to penetrate between 1 to 2 mm through the slot into the waveguide. This should ensure sufficient coupling to measure the electric field in the waveguide without disturbing the standing wave set up by the load under. 2.. Set the attenuator to approximately 20° to provide a fairly good value of buffer attenuation, switch the X-band source to internal keying and meter to detector output. Switch on the console power supply and the X-band oscillator.. 3.. Move the detector carriage along the slotted waveguide section to locate a position of an electric field maximum. Adjust the sensitivity of the detector-amplifier on the console to provide a meter reading of 3 to 4 mA. If necessary adjust the attenuator setting.. 4.. The microwave bench is now set up to measure the VSWR of the resistive load. Move the probe-detector carriage to a position closest to the load and then moving away from the load record positions of electric field minima and values of detector output current at positions of both minima and maxim. Record results in a table similar to that given in Figure 2.-4-6 below. With resistive load. With short-circuit. Positions of max. & min.. Detector Current. Positions of max. & min.. x1min =. Imin1 =. x1 s/c min =. x2max =. Imax2 =. x3min =. Imin3 =. x4max =. Imax4 =. x5min =. Imin5 =. x3 s/c min =. x5 s/c min =. Figure 2-4-6: Table for Recording Results for Impedance Measurement. 56-200. 2-4-9.

(65) Assignment 4 MICROWAVE TRAINER 5.. Measurement of Impedance and Impedance Matching Remove the resistive load and replace by the short-circuit plate R so that the slotted line is now terminated in a short-circuit. Locate and record positions of electric field minimum as the probe-detector carriage is moved along the slotted line starting closest to the short-circuit and moving progressively along the slot towards the source.. 6.. Calculate from your results the VSWR S of the load, the guide wavelength λg and the distance d of first electric field minimum from the load input. Remember: VSWR S =. Imax Imin. λg = 2 (x3s/c - x1s/c ) = x5s/c - X1s/c. (note: use short-circuit positions for lg since these are welldefined nulls and hence can be measured very accurately) d = x1 = x1s/c = x3 - x3s/c 7.. Finally calculate the normalised impedance of the load, zT = rT + j xT where the resistive part rT and imaginary part xT are given by the formulae (4) and (5) in the Introduction section.. 8.. Check your result using the Smith chart.. 2-4-10. 56-200.

(66) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching. Matching a waveguide load using a slotted waveguide probe tuner. Figure 2-4-7. 1.. Set up the equipment as shown in Figure 2-4-7 with the probe tuner C inserted between the slotted line and the resistive termination K. The probe-tuner unit is to be used to match the resistive load and improve its VSWR, ideally to unity.. 2.. The probe position is to be located where the real part of the normalised input admittance of the load is unity and the imaginary part (the susceptance) is inductive, i.e. when yin (l) = 1 - jb The inductive susceptance -jb can then be cancelled by introducing the probe at this point and adjusting the depth of penetration until the capacitive susceptance of the probe +jb cancels -jb. The resultant admittance,. 56-200. 2-4-11.

(67) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching. yin = 1 - jb + jb = 1 and so matching is achieved. 3.. The desired position of the probe-tuner is given by the formula in the Introduction section: l = d + lm + ½n lg where d = distance of first electric field minimum from load lm =. λg 2π. -1  1  tan    S. S = load VSWR n = 0, 1, 2, 3.... Using the results obtained in the previous impedance measurement section, calculate lm and locate the probe at the required position l. Notes: (i)The scale of the probe-tuner carriage unit zero is at 10mm from its right-hand flange, so the probe should be positioned at (l - 10) mm relative to this scale. (ii)The minimum practical value of l should be selected for most effective matching; the condition n = 0 is not usually physically obtainable so select n = 1 giving: l = d + ½lg. 4.. 2-4-12. Having set the probe at the position (l - 10) relative to the tuner scale gradually increase the probe penetration measuring the VSWR, at each position. With small penetration depths little improvement in VSWR is obtained. However, as the matching condition is approached where the capacitive susceptance of the probe cancels the load input susceptance a sharp decrease in VSWR can be observed.. 56-200.

(68) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching. Repeat the best value of VSWR and compare with the load VSWR before matching in terms of the percentage of the power reflected and percentage of power transmitted. 5.. Check the values of l and lm obtained above using a Smith chart.. SUMMARY. Methods of impedance measurement and matching have been investigated experimentally. The normalised impedance of a waveguide load has been measured and also matched using a shunt stub in the form of a probe tuner. Results may be processed analytically using transmission line formulae and also with the aid of a Smith chart.. 56-200. 2-4-13.

(69) Assignment 4 MICROWAVE TRAINER. Measurement of Impedance and Impedance Matching Notes. 2-4-14. 56-200.

(70) Assignment 4 MICROWAVE TRAINER. Typical Results and Answers. Measurement of resistive load impedance VSWR S = 1.63 position of minima with load 21.9,. 41.0,. 59.2 mm. positions of minima with short-circuit 27.9,. 46.3,. 65.1 mm. guide wavelength (average value) λg = 37.2 mm Position of first minimum from load d = 41 – 27.9 = 13.1 mm = 59.2 – 46.3 = 12.9 mm average value d = 13 mm d. λg βd = Calculation of normalised load impedance. =. 13 = 0.35 37.2. 2π. λg. d = 2π (0.35) rad or 126°. tanßd = tan 126° = -1.38; S = 1.63, S 2 = 2.66 Using formulae (4) and (5) in Introduction section:. 56-200. rT =. S(1 = tan 2 β d) 1.63(1 + 1.9) = = 1.03 2 2 2.66 + 1.9 S + tan β d. xT =. tan β d (1 - S2) - 1.38(1 − 2.66) = = 0.5 2 2 2.66 + 1.9 S + tan β d. 2-4-15.

(71) Assignment 4 MICROWAVE TRAINER. Typical Results and Answers. Calculation of normalised load impedance using a Smith chart 1.. Draw in the VSWR circle with S = 1.63, that is the circle centre point M (1, 0) on the chart cutting the vertical ρ axis at the point P = 1.63. See Smith chart of Figure 2.4.8.. 2.. To locate normalised impedance: (i) point Q where r = 1/S = 1/1.63 = 0.61 represents the input impedance of the load at electric field minimum. (ii) Move d/lg = 13/37.2 = 0.35 wavelengths from the point Q in the counter clockwise direction, that is the direction marked towards load on the chart. (iii) Locate 0.35 on outer wavelength scale, point K. Join K to centre point M. (iv) The point Z where the line KM cuts the VSWR circle provided the coordinates of the normalised impedance of the load: z = (1.05, 0.5) so rT = 1.05, xT = 0.5 and zT = 1.05 + j 0.5. 2-4-16. 56-200.

(72) Assignment 4 MICROWAVE TRAINER. Typical Results and Answers. Vswr circle S = 1.63. K (0.35). Figure 2-4-8:. Determination of load impedance using a Smith Chart. 56-200. 2-4-17.

(73) Assignment 4 MICROWAVE TRAINER. Typical Results and Answers. Matching results: matching resistive load using slotted guide probe tuner Calculation of probe tuner from load impedance measurements Normalised load impedance, calculated from previous results, is given in Figure 2-4-9. Distance of first minimum,. d = 13 mm. Guide wavelength. lg = 37.2 mm d/lg = 0.35. Load VSWR. S = 1.63. distance from minimum where input admittance is yin = 1 - jb, that is at the plane where matching is to be effected is given by: lm =. =. =. λg -1 1 tan 2π S 1 λg -1 tan 2π 1.63. λg -1 tan (0.783)= 0.1λg 2π. Thus total distance from load for matching plane: l = lm + d = 0.1 lg + 0.35 lg = 0.45 lg and this is repeated at further ½ lg intervals in the direction towards generator. Hence matching positions are: l = 0.45 lg = 0.45 x 37.2 = 16.7 mm l = 0.45 lg + 0.5 lg = 0.95 lg = 35.3 mm l = 0.45 lg 1.0 lg = 1.45 lg = 53.9 mm. 2-4-18. 56-200.

(74) Assignment 4 MICROWAVE TRAINER. Typical Results and Answers and allowing for 10 mm displacement of tuner scale zero, the tuner probe should be placed at 6.7 mm or 25.3 mm of 43.9 mm to effect matching. Selecting position 25.3 mm the following improvement in VSWR was obtained: probe penetration referenced to micrometer scale: 16.96 mm VSWR measured, S = 12 Thus matching has improved VSWR from 1.63 to 1.2: without matching: VSWR. S = 1.2. reflection coefficient G = S-1/S+1 = 0.3 percentage of power reflected, G2 x 100 = 9% with matching: VSWR. S = 1.2. G = S-1/S+2 = 0.091 percentage of power reflected, less than 1% Matching using Smith Chart. The steps described below refer to the Smith chart of Figure 2.4.9 used to execute the matching calculations.. 1.. Draw VSWR circle with S = 1.63 and locate load impedance by moving d/lg = 0.35 wavelengths in the direction towards the load from the position Q on the r-axis, r = 1/S = 0.61.. 2.. Load impedance is at point Z, zT = 1.05 + j0.5 Load admittance is diagonally opposite at point Y, yT = 0.78 - j0.36. 56-200. 2-4-19.

(75) Assignment 4 MICROWAVE TRAINER. 3.. Typical Results and Answers. Next locate point on the VSWR circle where this circle cuts the resistive/conductive unity of 1.0 circle, i.e. point T. Draw in the line MT. At point T the normalised input admittance, y = 1 –jb has a conductance of 1.0 and an inductive susceptance -jb which can be determined from reading off the Smith chart at T: –jb = –j 0.48 for this particular case. The inductive susceptance is cancelled by the probe tuner introducing an equal and opposite sign capacitive susceptance.. 4.. The position of the probe of the tuner relative to the plane of the load is determined from the Smith chart: reference position of load admittance, point Y : 0.044 wavelengths matching position of tuner, point T : 0.356 wavelengths so distance of tuner from load = (0.044 + 0.356) lg = 0.40 lg. 5.. 2-4-20. Note that the matching position is repeated at subsequent intervals of ½ lg from T towards the generator. Correct must also be made for the zero of the tuner scale which is situated 10mm from the plane of the load.. 56-200.

(76) Assignment 4 MICROWAVE TRAINER. Typical Results and Answers. Yr = 0.78-j0.36. Y Z T 2 T = 1.05 f j 0.5 0.356. Figure 2-4-9:. Determination of matching position for shunt stub using a Smith chart. 56-200. 2-4-21.

(77) Assignment 4 MICROWAVE TRAINER. Typical Results and Answers. Notes. 2-4-22. 56-200.

(78) Assignment 5 MICROWAVE TRAINER. CONTENT. Horn Antenna Investigations. A test bench is set up to investigate the radiation pattern of a rectangular waveguide pyramidal horn antenna. Polar radiation diagrams are plotted and the 3 dB beamwidth of the antenna is determined.. EQUIPMENT REQUIRED. OBJECTIVES. KNOWLEDGE LEVEL. 56-200. Qty. Identifying Letter. Description. 1. -. Control console. 1. A. Variable attenuator. 1. K. Resistive load termination. 1. M. Diode detector. 2. N. Horn antenna. 1. P. X-band oscillator. 4. -. Supports. When you have completed this assignment you . Will appreciated the directional radiation characteristics of a horn antenna and know how to plot its radiation pattern. . Know how to measure the beamwidth and gain of an antenna. Before you start this assignment it would be an advantage . To be familiar with the operation of the microwave bench. . Know that microwave signals can be detected using a diode detector and for low-level signals, that detected output is proportional to power. . To appreciate the role of antennas in the transmission and reception of radio waves. 2-5-1.

(79) Assignment 5 MICROWAVE TRAINER INTRODUCTION. Horn Antenna Investigations Antennas are essential components in the transmission and reception of radio waves. In the microwave range, highly directive antennas capable of producing the narrow beams required for the line-of-sight links and satellite communications can be designed. The horn antenna, whose radiation characteristics are investigated in this assignment, plays an important role as a radiator of microwave energy in its own right and also as a primary feed for reflector antennas employed in microwave radio links and radar. The directional characteristics of an antenna - the directions it radiates energy into space - can be visualised graphically by plotting radiated power density versus angular direction. These polar plots are known as far-field radiation diagrams, the latter qualifying the condition that measurements are taken at a sufficiently far distance from the antenna to represent the characteristics as dependent primarily on angular direction. Close to an antenna the radiation pattern is very complex and seldom used in practice. The far-field conditions are satisfied at distances, r ≥ 2D2 / λ where D = largest antenna dimension λ = transmitted wavelength To fully describe the directional properties of an antenna two radiation diagrams are normally required: one in the horizontal plane, in the case of the horn antenna this would be the H-plane with respect to the horn sketched in Figure 2-5-1, and one for the vertical plane, the E-plane in Figure 2-5-1.. Figure 2-5-1: Pyramidal Horn Antenna. 2-5-2. 56-200.

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